The contripetal force F acting on a particle moving uniformly in a circle may depend upon mass (m), velocity (v) and redio ( r) of the circle . Derive the formula for F using the method of dimensions.

Explanation

To derive the formula for centripetal force \( F \) using the method of dimensions, we will follow these steps:

### Step 1: Identify the variables
The centripetal force \( F \) may depend on mass \( m \), velocity \( v \), and radius \( r \). We can express this relationship as:
\[ F = k \cdot m^a \cdot v^b \cdot r^c \]
where \( k \) is a dimensionless constant, and \( a, b, c \) are the powers to be determined.
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